Page:SahaElectrodynamics.djvu/24

This equation expresses the law of observation in its most general form. If $\Phi ={\frac {\pi }{2}}$, the equation takes the simple form

$\cos \Phi '=-{\frac {v}{c}}$.

We have still to investigate the amplitude of the waves, which occur in these equations. If A and A' be the amplitudes in the stationary and the moving systems (either electrical or magnetic), we have

$A'^{2}=A^{2}{\frac {\left(1-{\frac {v}{c}}\cos \Phi \right)^{2}}{1-{\frac {v^{2}}{c^{2}}}}}$.

If $\Phi =0$, this reduces to the simple form

$A'^{2}=A^{2}{\frac {1-{\frac {v}{c}}}{1+{\frac {v}{c}}}}$.

From these equations, it appears that for an observer, which moves with the velocity c towards the source of light, the source should appear infinitely intense.

§ 8. Transformation of the Energy of the Rays of Light. Theory of the Radiation-pressure on a perfect mirror.

Since ${\frac {A^{2}}{8\pi }}$ is equal to the energy of light per unit volume, we have to regard ${\frac {A}{8\pi }}$ as the energy of light in